Think tic-tac-toe board and you'll see the rule-of-thirds -- put the main subject at one of the intersection points and the horizon line on one of the horizontal lines. If you're shooting people you try to get their eyes on the top horizontal line.

If the subject is looking or moving in a specific direction you definitely want to give them room in the frame to move the way they are looking -- otherwise it looks like they're going to fall off the map, which is scary.